This paper describes the implementation and performance of a particle flow algorithm applied to 20.2 fb\(^{-1}\) of ATLAS data from 8 TeV proton–proton collisions in Run 1 of the LHC. The algorithm removes calorimeter energy deposits due to charged hadrons from consideration during jet reconstruction, instead using measurements of their momenta from the inner tracker. This improves the accuracy of the charged-hadron measurement, while retaining the calorimeter measurements of neutral-particle energies. The paper places emphasis on how this is achieved, while minimising double-counting of charged-hadron signals between the inner tracker and calorimeter. The performance of particle flow jets, formed from the ensemble of signals from the calorimeter and the inner tracker, is compared to that of jets reconstructed from calorimeter energy deposits alone, demonstrating improvements in resolution and pile-up stability.

Jet reconstruction and performance using particle flow with the ATLAS Detector

Eur. Phys. J. C
Jet reconstruction and performance using particle flow with the ATLAS Detector
ATLAS Collaboration 0
0 CERN , 1211 Geneva 23 , Switzerland
1 Also at Physics Department, An-Najah National University , Nablus, Palestine
2 Also at TRIUMF , Vancouver, BC , Canada
3 Also at Department of Physics and Astronomy, University of Louisville , Louisville, KY , USA
4 Also at Institute of Physics, Azerbaijan Academy of Sciences , Baku , Azerbaijan
5 Also at Novosibirsk State University , Novosibirsk , Russia
6 Also at Department of Physics, King's College London , London , UK
This paper describes the implementation and performance of a particle flow algorithm applied to 20.2 fb−1 of ATLAS data from 8 TeV proton-proton collisions in Run 1 of the LHC. The algorithm removes calorimeter energy deposits due to charged hadrons from consideration during jet reconstruction, instead using measurements of their momenta from the inner tracker. This improves the accuracy of the charged-hadron measurement, while retaining the calorimeter measurements of neutral-particle energies. The paper places emphasis on how this is achieved, while minimising double-counting of charged-hadron signals between the inner tracker and calorimeter. The performance of particle flow jets, formed from the ensemble of signals from the calorimeter and the inner tracker, is compared to that of jets reconstructed from calorimeter energy deposits alone, demonstrating improvements in resolution and pile-up stability.
-
Contents
1 Introduction
Jets are a key element in many analyses of the data collected
by the experiments at the Large Hadron Collider (LHC) [
1
].
The jet calibration procedure should correctly determine the
jet energy scale and additionally the best possible energy and
angular resolution should be achieved. Good jet
reconstruction and calibration facilitates the identification of known
resonances that decay to hadronic jets, as well as the search
for new particles. A complication, at the high luminosities
encountered by the ATLAS detector [
2
], is that multiple
interactions can contribute to the detector signals associated with
a single bunch-crossing (pile-up). These interactions, which
are mostly soft, have to be separated from the hard interaction
that is of interest.
Pile-up contributes to the detector signals from the
collision environment, and is especially important for
higherintensity operations of the LHC. One contribution arises
from particle emissions produced by the additional proton–
proton ( pp) collisions occurring in the same bunch crossing
as the hard-scatter interaction (in-time pile-up). Further
pileup influences on the signal are from signal remnants in the
ATLAS calorimeters from the energy deposits in other bunch
crossings (out-of-time pile-up).
In Run 1 of the LHC, the ATLAS experiment used either
solely the calorimeter or solely the tracker to reconstruct
hadronic jets and soft particle activity. The vast majority of
analyses utilised jets that were built from topological
clusters of calorimeter cells (topo-clusters) [
3
]. These jets were
then calibrated to the particle level using a jet energy scale
(JES) correction factor [
4–7
]. For the final Run 1 jet
calibration, this correction factor also took into account the tracks
associated with the jet, as this was found to greatly improve
the jet resolution [4]. ‘Particle flow’ introduces an
alternative approach, in which measurements from both the tracker
and the calorimeter are combined to form the signals, which
ideally represent individual particles. The energy deposited
in the calorimeter by all the charged particles is removed. Jet
reconstruction is then performed on an ensemble of ‘particle
flow objects’ consisting of the remaining calorimeter energy
and tracks which are matched to the hard interaction.
The chief advantages of integrating tracking and
calorimetric information into one hadronic reconstruction step are
as follows:
• The design of the ATLAS detector [
8
] specifies a
calorimeter energy resolution for single charged pions
in the centre of the detector of
50%
= √E
⊕ 3.4% ⊕
1%
E
,
while the design inverse transverse momentum resolution
for the tracker is
σ
1
pT
· pT = 0.036% · pT ⊕ 1.3%,
where energies and transverse momenta are measured in
GeV. Thus for low-energy charged particles, the
momentum resolution of the tracker is significantly better than
the energy resolution of the calorimeter. Furthermore,
the acceptance of the detector is extended to softer
particles, as tracks are reconstructed for charged particles
with a minimum transverse momentum pT > 400 MeV,
whose energy deposits often do not pass the noise
thresholds required to seed topo-clusters [
9
].
(1)
(2)
• The angular resolution of a single charged particle,
reconstructed using the tracker is much better than that of the
calorimeter.
• Low- pT charged particles originating within a hadronic
jet are swept out of the jet cone by the magnetic field by
the time they reach the calorimeter. By using the track’s
azimuthal coordinate1 at the perigee, these particles are
clustered into the jet.
• When a track is reconstructed, one can ascertain whether
it is associated with a vertex, and if so the vertex from
which it originates. Therefore, in the presence of multiple
in-time pile-up interactions, the effect of additional
particles on the hard-scatter interaction signal can be mitigated
by rejecting signals originating from pile-up vertices.2
The capabilities of the tracker in reconstructing charged
particles are complemented by the calorimeter’s ability to
reconstruct both the charged and neutral particles. At high
energies, the calorimeter’s energy resolution is superior to the
tracker’s momentum resolution. Thus a combination of the
two subsystems is preferred for optimal event
reconstruction. Outside the geometrical acceptance of the tracker, only
the calorimeter information is available. Hence, in the
forward region the topo-clusters alone are used as inputs to the
particle flow jet reconstruction.
However, particle flow introduces a complication. For any
particle whose track measurement ought to be used, it is
necessary to correctly identify its signal in the calorimeter, to
avoid double-counting its energy in the reconstruction. In
the particle flow algorithm described herein, a Boolean
decision is made as to whether to use the tracker or
calorimeter measurement. If a particle’s track measurement is to be
used, the corresponding energy must be subtracted from the
calorimeter measurement. The ability to accurately subtract
all of a single particle’s energy, without removing any energy
deposited by any other particle, forms the key performance
criterion upon which the algorithm is optimised.
Particle flow algorithms were pioneered in the ALEPH
experiment at LEP [
10
]. They have also been used in the
H1 [
11
], ZEUS [
12, 13
] and DELPHI [14] experiments.
Subsequently, they were used for the reconstruction of hadronic
τ -lepton decays in the CDF [
15
], D0 [
16
] and ATLAS [
17
]
1 ATLAS uses a right-handed coordinate system with its origin at the
nominal interaction point (IP) in the centre of the detector and the z-axis
along the beam direction. The x-axis points from the IP to the centre
of the LHC ring, and the y-axis points upward. Cylindrical coordinates
(r, φ) are used in the transverse plane, φ being the azimuthal angle
around the z-axis. The pseudorapidity is defined in terms of the polar
angle θ as η = − ln tan(θ/2). Angular distance is measured in units of
R = ( φ)2 + ( η)2.
2 The standard ATLAS reconstruction defines the hard-scatter primary
vertex to be the primary vertex with the largest pT2 of the associated
tracks. All other primary vertices are considered to be contributed by
pile-up.
experiments. In the CMS experiment at the LHC, large gains
in the performance of the reconstruction of hadronic jets and
τ leptons have been seen from the use of particle flow
algorithms [
18–20
]. Particle flow is a key ingredient in the design
of detectors for the planned International Linear Collider [
21
]
and the proposed calorimeters are being optimised for its
use [
22
]. While the ATLAS calorimeter already measures jet
energies precisely [
6
], it is desirable to explore the extent to
which particle flow is able to further improve the ATLAS
hadronic-jet reconstruction, in particular in the presence of
pile-up interactions.
This paper is organised as follows. A description of the
detector is given in Sect. 2, the Monte Carlo (MC) simulated
event samples and the dataset used are described in Sects. 3
and 4, while Sect. 5 outlines the relevant properties of
topoclusters. The particle flow algorithm is described in Sect. 6.
Section 7 details the algorithm’s performance in energy
subtraction at the level of individual particles in a variety of
cases, starting from a single pion through to dijet events. The
building and calibration of reconstructed jets is covered in
Sect. 8. The improvement in jet energy and angular
resolution is shown in Sect. 9 and the sensitivity to pile-up is
detailed in Sect. 10. A comparison between data and MC
simulation is shown in Sect. 11 before the conclusions are
presented in Sect. 12.
2 ATLAS detector
The ATLAS experiment features a multi-purpose detector
designed to precisely measure jets, leptons and photons
produced in the pp collisions at the LHC. From the inside out,
the detector consists of a tracking system called the inner
detector (ID), surrounded by electromagnetic (EM) sampling
calorimeters. These are in turn surrounded by hadronic
sampling calorimeters and an air-core toroid muon spectrometer
(MS). A detailed description of the ATLAS detector can be
found in Ref. [
2
].
The high-granularity silicon pixel detector covers the
vertex region and typically provides three measurements
per track. It is followed by the silicon microstrip tracker
which usually provides eight hits, corresponding to four
two-dimensional measurement points, per track. These
silicon detectors are complemented by the transition radiation
tracker, which enables radially extended track
reconstruction up to |η| = 2.0. The ID is immersed in a 2 T axial
magnetic field and can reconstruct tracks within the
pseudorapidity range |η| < 2.5. For tracks with transverse momentum
pT < 100 GeV, the fractional inverse momentum resolution
σ (1/ pT)· pT measured using 2012 data, ranges from
approximately 2–12% depending on pseudorapidity and pT [
23
].
The calorimeters provide hermetic azimuthal coverage
in the range |η| < 4.9. The detailed structure of the
calorimeters within the tracker acceptance strongly
influences the development of the shower subtraction algorithm
described in this paper. In the central barrel region of the
detector, a high-granularity liquid-argon (LAr)
electromagnetic calorimeter with lead absorbers is surrounded by a
hadronic sampling calorimeter (Tile) with steel absorbers and
active scintillator tiles. The same LAr technology is used
in the calorimeter endcaps, with fine granularity and lead
absorbers for the EM endcap (EMEC), while the hadronic
endcap (HEC) utilises copper absorbers with reduced
granularity. The solid angle coverage is completed with forward
copper/LAr and tungsten/LAr calorimeter modules (FCal)
optimised for electromagnetic and hadronic measurements
respectively. Figure 1 shows the physical location of the
different calorimeters. To achieve a high spatial resolution,
φ of all the different ATLAS calorimeter layers relevant to the tracking coverage of the inner detector
EM LAr calorimeter
Barrel
Presampler
PreSamplerB/E
1st layer
EMB1/EME1
2nd layer
EMB2/EME2
3rd layer
EMB3/EME3
1st layer
TileBar0/TileExt0
2nd layer
TileBar1/TileExt1
3rd layer
TileBar2/TileExt2
1st layer
HEC0
2nd layer
HEC1
3rd layer
HEC2
4th layer
HEC3
the calorimeter cells are arranged in a projective geometry
with fine segmentation in φ and η. Additionally, each of
the calorimeters is longitudinally segmented into multiple
layers, capturing the shower development in depth. In the
region |η| < 1.8, a presampler detector is used to correct
for the energy lost by electrons and photons upstream of the
calorimeter. The presampler consists of an active LAr layer of
thickness 1.1 cm (0.5 cm) in the barrel (endcap) region. The
granularity of all the calorimeter layers within the tracker
acceptance is given in Table 1.
The EM calorimeter is over 22 radiation lengths in depth,
ensuring that there is little leakage of EM showers into
the hadronic calorimeter. The total depth of the complete
calorimeter is over 9 interaction lengths in the barrel and over
10 interaction lengths in the endcap, such that good
containment of hadronic showers is obtained. Signals in the MS are
used to correct the jet energy if the hadronic shower is not
completely contained. In both the EM and Tile calorimeters,
most of the absorber material is in the second layer. In the
hadronic endcap, the material is more evenly spread between
the layers.
The muon spectrometer surrounds the calorimeters and is
based on three large air-core toroid superconducting magnets
with eight coils each. The field integral of the toroids ranges
from 2.0 to 6.0 Tm across most of the detector. It includes a
system of precision tracking chambers and fast detectors for
triggering.
3 Simulated event samples
A variety of MC samples are used in the optimisation and
performance evaluation of the particle flow algorithm. The
simplest samples consist of a single charged pion generated
with a uniform spectrum in the logarithm of the generated
pion energy and in the generated η. Dijet samples generated
with Pythia 8 (v8.160) [
24, 25
], with parameter values set
to the ATLAS AU2 tune [
26
] and the CT10 parton
distribution functions (PDF) set [
27
], form the main samples used to
derive the jet energy scale and determine the jet energy
resolution in simulation. The dijet samples are generated with
a series of jet pT thresholds applied to the leading jet,
reconstructed from all stable final-state particles excluding muons
and neutrinos, using the anti-kt algorithm [
28
] with radius
parameter 0.6 using FastJet (v3.0.3) [
29, 30
].
For comparison with collision data, Z → μμ events are
generated with Powheg- Box (r1556) [
31
] using the CT10
PDF and are showered with Pythia 8, with the ATLAS AU2
tune. Additionally, top quark pair production is simulated
with MC@NLO (v4.03) [
32, 33
] using the CT10 PDF set,
interfaced with Herwig (v6.520) [
34
] for parton showering,
and the underlying event is modelled by Jimmy (v4.31) [
35
].
The top quark samples are normalised using the cross-section
calculated at next-to-next-to-leading order (NNLO) in QCD
including resummation of next-to-next-to-leading
logarithmic soft gluon terms with top++2.0 [
36–43
], assuming a top
quark mass of 172.5 GeV. Single-top-quark production
processes contributing to the distributions shown are also
simulated, but their contributions are negligible.
3.1 Detector simulation and pile-up modelling
All samples are simulated using Geant4 [
44
] within the
ATLAS simulation framework [
45
] and are reconstructed
using the noise threshold criteria used in 2012 data-taking [3].
Single-pion samples are simulated without pile-up, while
dijet samples are simulated under three conditions: with no
pile-up; with pile-up conditions similar to those in the 2012
data; and with a mean number of interactions per bunch
crossing μ = 40, where μ follows a Poisson distribution. In
2012, the mean value of μ was 20.7 and the actual number of
interactions per bunch crossing ranged from around 10 to 35
depending on the luminosity. The bunch spacing was 50 ns.
When compared to data, the MC samples are reweighted to
have the same distribution of μ as present in the data. In all
the samples simulated including pile-up, effects from both
the same bunch crossing and previous/subsequent crossings
are simulated by overlaying additional generated
minimumbias events on the hard-scatter event prior to reconstruction.
The minimum-bias samples are generated using Pythia 8
with the ATLAS AM2 tune [
46
] and the MSTW2009 PDF
set [
47
], and are simulated using the same software as the
hard-scatter event.
3.2 Truth calorimeter energy and tracking information
For some samples the full Geant4 hit information [
44
] is
retained for each calorimeter cell such that the true amount
of hadronic and electromagnetic energy deposited by each
generated particle is known. Only the measurable hadronic
and electromagnetic energy deposits are counted, while the
energy lost due to nuclear capture and particles escaping from
the detector is not included. For a given charged pion the sum
of these hits in a given cluster i originating from this particle
is denoted by Etcrluues,iπ .
Reconstructed topo-cluster energy is assigned to a given
truth particle according to the proportion of Geant4 hits
supplied to that topo-cluster by that particle. Using the Geant4
hit information in the inner detector a track is matched to a
generated particle based on the fraction of hits on the track
which originate from that particle [
48
].
4 Data sample
Data acquired during the period from March to December
2012 with the LHC operating at a pp centre-of-mass energy
of 8 TeV are used to evaluate the level of agreement between
data and Monte Carlo simulation of different outputs of the
algorithm. Two samples with a looser preselection of events
are reconstructed using the particle flow algorithm. A tighter
selection is then used to evaluate its performance.
First, a Z → μμ enhanced sample is extracted from
the 2012 dataset by selecting events containing two
reconstructed muons [
49
], each with pT > 25 GeV and |η| < 2.4,
where the invariant mass of the dimuon pair is greater than
55 GeV, and the pT of the dimuon pair is greater than 30
GeV.
Similarly, a sample enhanced in t t¯ → bb¯qq¯ μν events
is obtained from events with an isolated muon and at least
one hadronic jet which is required to be identified as a jet
containing b-hadrons (b-jet). Events are selected that pass
single-muon triggers and include one reconstructed muon
satisfying pT > 25 GeV, |η| < 2.4, for which the sum
of additional track momenta in a cone of size R = 0.2
around the muon track is less than 1.8 GeV. Additionally, a
reconstructed calorimeter jet is required to be present with
pT > 30 GeV, |η| < 2.5, and pass the 70% working point
of the MV1 b-tagging algorithm [
50
].
For both datasets, all ATLAS subdetectors are required to
be operational with good data quality. Each dataset
corresponds to an integrated luminosity of 20.2 fb−1. To remove
events suffering from significant electronic noise issues,
cosmic rays or beam background, the analysis excludes
events that contain calorimeter jets with pT > 20 GeV
which fail to satisfy the ‘looser’ ATLAS jet quality
criteria [
51, 52
].
5 Topological clusters
The lateral and longitudinal segmentation of the calorimeters
permits three-dimensional reconstruction of particle
showers, implemented in the topological clustering algorithm [
3
].
Topo-clusters of calorimeter cells are seeded by cells whose
absolute energy measurements |E | exceed the expected noise
by four times its standard deviation. The expected noise
includes both electronic noise and the average contribution
from pile-up, which depends on the run conditions. The
topoclusters are then expanded both laterally and longitudinally
in two steps, first by iteratively adding all adjacent cells with
absolute energies two standard deviations above noise, and
finally adding all cells neighbouring the previous set. A
splitting step follows, separating at most two local energy
maxima into separate topo-clusters. Together with the ID tracks,
these topo-clusters form the basic inputs to the particle flow
algorithm.
The topological clustering algorithm employed in ATLAS
is not designed to separate energy deposits from different
particles, but rather to separate continuous energy showers
of different nature, i.e. electromagnetic and hadronic, and
also to suppress noise. The cluster-seeding threshold in the
topo-clustering algorithm results in a large fraction of
lowenergy particles being unable to seed their own clusters. For
example, in the central barrel ∼25% of 1 GeV charged pions
do not seed their own cluster [
9
].
While the granularity, noise thresholds and employed
technologies vary across the different ATLAS calorimeters,
they are initially calibrated to the electromagnetic scale (EM
scale) to give the same response for electromagnetic
showers from electrons or photons. Hadronic interactions produce
responses that are lower than the EM scale, by amounts
depending on where the showers develop. To account for
this, the mean ratio of the energy deposited by a particle to
the momentum of the particle is determined based on the
position of the particle’s shower in the detector, as described
in Sect. 6.4.
A local cluster (LC) weighting scheme is used to calibrate
hadronic clusters to the correct scale [
3
]. Further
development is needed to combine this with particle flow; therefore,
in this work the topo-clusters used in the particle flow
algorithm are calibrated at the EM scale.
6 Particle flow algorithm
A cell-based energy subtraction algorithm is employed to
remove overlaps between the momentum and energy
measurements made in the inner detector and calorimeters,
respectively. Tracking and calorimetric information is
combined for the reconstruction of hadronic jets and soft
activity (additional hadronic recoil below the threshold used in
jet reconstruction) in the event. The reconstruction of the
soft activity is important for the calculation of the missing
transverse momentum in the event [
53
], whose magnitude is
denoted by E miss.
T
The particle flow algorithm provides a list of tracks and
a list of topo-clusters containing both the unmodified
topoclusters and a set of new topo-clusters resulting from the
energy subtraction procedure. This algorithm is sketched
in Fig. 2. First, well-measured tracks are selected
following the criteria discussed in Sect. 6.2. The algorithm then
attempts to match each track to a single topo-cluster in the
calorimeter (Sect. 6.3). The expected energy in the
calorimeter, deposited by the particle that also created the track, is
computed based on the topo-cluster position and the track
momentum (Sect. 6.4). It is relatively common for a
single particle to deposit energy in multiple topo-clusters. For
each track/topo-cluster system, the algorithm evaluates the
probability that the particle energy was deposited in more
than one topo-cluster. On this basis it decides if it is
necessary to add more topo-clusters to the track/topo-cluster
system to recover the full shower energy (Sect. 6.5). The
Fig. 2 A flow chart of how the particle flow algorithm proceeds,
starting with track selection and continuing until the energy associated with
the selected tracks has been removed from the calorimeter. At the end,
charged particles, topo-clusters which have not been modified by the
algorithm, and remnants of topo-clusters which have had part of their
energy removed remain
expected energy deposited in the calorimeter by the particle
that produced the track is subtracted cell by cell from the set
of matched topo-clusters (Sect. 6.6). Finally, if the remaining
energy in the system is consistent with the expected shower
fluctuations of a single particle’s signal, the topo-cluster
remnants are removed (Sect. 6.7).
This procedure is applied to tracks sorted in descending
pT-order, firstly to the cases where only a single topo-cluster
is matched to the track, and then to the other selected tracks.
This methodology is illustrated in Fig. 3.
Details about each step of the procedure are given in the
rest of this section. After some general discussion of the
properties of topo-clusters in the calorimeter, the energy
subtraction procedure for each track is described. The
procedure is accompanied by illustrations of performance metrics
used to validate the configuration of the algorithm. The
samples used for the validation are single-pion and dijet MC
samples without pile-up, as described in the previous
section. Charged pions dominate the charged component of
the jet, which on average makes up two-thirds of the
visible jet energy [
54, 55
]. Another quarter of the jet energy
is contributed by photons from neutral hadron decays, and
the remainder is carried by neutral hadrons that reach the
calorimeter. Because the majority of tracks are generated by
charged pions [
56
], particularly at low pT, the pion mass
hypothesis is assumed for all tracks used by the particle
flow algorithm to reconstruct jets. Likewise the energy
subtraction is based on the calorimeter’s response to charged
pions.
In the following sections, the values for the parameter
set and the performance obtained for the 2012 dataset are
discussed. These parameter values are not necessarily the
product of a full optimisation, but it has been checked that
the performance is not easily improved by variations of these
choices. Details of the optimisation are beyond the scope of
the paper.
6.1 Containment of showers within a single topo-cluster
The performance of the particle flow algorithm, especially
the shower subtraction procedure, strongly relies on the
topological clustering algorithm. Hence, it is important to
quantify the extent to which the clustering algorithm
distinguishes individual particles’ showers and how often it
splits a single particle’s shower into more than one
topocluster. The different configurations of topo-clusters
containing energy from a given single pion are classified using two
variables.
For a given topo-cluster i , the fraction of the particle’s
true energy contained in the topo-cluster (see Sect. 3.2), with
respect to the total true energy deposited by the particle in
all clustered cells, is defined as
(3)
(4)
εiclus
Etcrluues,iπ
= Etarluleto,pπo−clusters ,
where Etcrluues,iπ is the true energy deposited in topo-cluster i by
the generated particle under consideration and Etarluleto,pπo−clusters
is the true energy deposited in all topo-clusters by that truth
particle. For each particle, the topo-cluster with the highest
value of εiclus is designated the leading topo-cluster, for which
εlcelauds = εiclus. The minimum number of topo-clusters needed
to capture at least 90% of the particle’s true energy, i.e. such
that in=0 εiclus > 90%, is denoted by nc9l0us.
Topo-clusters can contain contributions from multiple
particles, affecting the ability of the subtraction algorithm to
separate the energy deposits of different particles. The purity
ρiclus for a topo-cluster i is defined as the fraction of true
energy within the topo-cluster which originates from the
particle of interest:
ρiclus
=
Etcrluues,iπ
Etcrluues,iall particles
.
For the leading topo-cluster, defined by having the highest
εiclus, the purity value is denoted by ρlcelauds.
Only charged particles depositing significant energy (at
least 20% of their true energy) in clustered cells are
considered in the following plots, as in these cases there is
significant energy in the calorimeter to remove. This also avoids the
case where insufficient energy is present in any cell to form
a cluster, which happens frequently for very low-energy
particles [
3
].
Figure 3 illustrates how the subtraction procedure is
designed to deal with cases of different complexity. Four
different scenarios are shown covering cases where the charged
pion deposits its energy in one cluster, in two clusters, and
where there is a nearby neutral pion which either deposits its
energy in a separate cluster or the same cluster as the charged
pion.
Several distributions are plotted for the dijet sample in
which the energy of the leading jet, measured at truth level,
is in the range 20 < plead < 500 GeV. The distribution of
T
εlcelauds is shown in Fig. 4 for different ptrue and ηtrue bins.
T
It can be seen that εlcelauds decreases as the pT of the particle
increases and very little dependence on η is observed. Figure
5 shows the distribution of nc9l0us. As expected, nc9l0us increases
with particle pT. It is particularly interesting to know the
fraction of particles for which at least 90% of the true energy
is contained in a single topo-cluster (nc9l0us = 1) and this is
shown in Fig. 6. Lastly, Fig. 7 shows the distribution of ρlcelauds.
This decreases as ptrue increases and has little dependence
T
on |ηtrue|.
For more than 60% of particles with 1 < ptrue < 2 GeV,
T
the shower is entirely contained within a single topo-cluster
the π +, while those in black are yet to be selected. The different layers
in the electromagnetic calorimeter (Presampler, EMB1, EMB2, EMB3)
are indicated. In this sketch only the first two layers of the Tile
calorimeter are shown (TileBar0 and TileBar1)
Fig. 5 Distributions of the number of topo-clusters required to
contain > 90% of the true deposited energy of a single charged pion which
deposits significant energy (20% of the particle’s energy) in the
clustered cells. The distributions are shown for three ptrue bins in three
T
(εlcelauds ∼ 1). This fraction falls rapidly with particle pT,
reaching ∼ 25% for particles in the range 5 < ptrue < 10 GeV. For
T
particles with ptrue < 2 GeV, 90% of the particle energy can
T
be captured within two topo-clusters in ∼ 95% of cases. The
topo-cluster purity also falls as the pion pT increases, with
the target particle only contributing between 38 and 45% of
the topo-cluster energy when 5 < ptrue < 10 GeV. This is in
T
part due to the tendency for high- pT particles to be produced
in dense jets, while softer particles from the underlying event
tend to be isolated from nearby activity.
In general, the subtraction of the hadronic shower is easier
for cases with topo-clusters with high ρiclus, and high εiclus,
since in this configuration the topo-clustering algorithm has
separated out the contributions from different particles.
6.2 Track selection
Tracks are selected which pass stringent quality criteria: at
least nine hits in the silicon detectors are required, and tracks
without pile-up with 20 < plead < 500 GeV and the statistical
uncer
T
tainties on the number of MC simulated events are shown as a hatched
band
|ηtrue| regions. The data are taken from a dijet sample without pile-up
with 20 < plead < 500 GeV and the statistical uncertainties on the
T
number of MC simulated events are shown as a hatched band
must have no missing Pixel hits when such hits would be
expected [
57
]. This selection is designed such that the
number of badly measured tracks is minimised and is referred
to as ‘tight selection’. No selection cuts are made on the
association to the hard scatter vertex at this stage
Additionally, tracks are required to be within |η| < 2.5 and have
pT > 0.5 GeV. These criteria remain efficient for tracks
from particles which are expected to deposit energy below
the threshold needed to seed a topo-cluster or particles that
do not reach the calorimeter. Including additional tracks by
reducing the pT requirement to 0.4 GeV leads to a
substantial increase in computing time without any corresponding
improvement in jet resolution. This is due to their small
contribution to the total jet pT.
Tracks with pT > 40 GeV are excluded from the
algorithm, as such energetic particles are often poorly isolated
from nearby activity, compromising the accurate removal
of the calorimeter energy associated with the track. In such
cases, with the current subtraction scheme, there is no
advan
1
)
1
90 =lcsu 0.9
Fig. 6 The probability that a single topo-cluster contains > 90% of
the true deposited energy of a single charged pion, which deposits
significant energy (20% of the particle’s energy) in the clustered cells.
The distributions are shown as a function of pTtrue in three |ηtrue|
regions. The data are taken from a dijet sample without pile-up with
20 < plead < 500 GeV and the statistical uncertainties on the number
T
of MC simulated events are shown as a hatched band
tage in using the tracker measurement. This requirement was
tuned both by monitoring the effectiveness of the energy
subtraction using the true energy deposited in dijet MC events,
and by measuring the jet resolution in MC simulation. The
majority of tracks in jets with pT between 40 and 60 GeV
have pT below 40 GeV, as shown later in Sect. 11.
In addition, any tracks matched to candidate electrons [
58
]
or muons [
49
], without any isolation requirements, identified
with medium quality criteria, are not selected and therefore
are not considered for subtraction, as the algorithm is
optimised for the subtraction of hadronic showers. The energy
deposited in the calorimeter by electrons and muons is hence
taken into account in the particle flow algorithm and any
resulting topo-clusters are generally left unsubtracted.
Figure 8 shows the charged-pion track reconstruction
efficiency, for the tracks selected with the criteria described
above, as a function of ηtrue and ptrue in the dijet MC sample,
T
with leading jets in the range 20 < plead < 1000 GeV and
T
with similar pile-up to that in the 2012 data. The Monte Carlo
generator information is used to match the reconstructed
tracks to the generated particles [
48
]. The application of the
tight quality criteria substantially reduces the rate of poorly
measured tracks, as shown in Fig. 9. Additionally, using the
above selection, the fraction of combinatorial fake tracks
arising from combining ID hits from different particles is
negligible [
48
].
6.3 Matching tracks to topo-clusters
To remove the calorimeter energy where a particle has formed
a single topo-cluster, the algorithm first attempts to match
each selected track to one topo-cluster. The distances φ and
η between the barycentre of the topo-cluster and the track,
extrapolated to the second layer of the EM calorimeter, are
computed for each topo-cluster. The topo-clusters are ranked
based on the distance metric
R =
,
ση
(5)
where ση and σφ represent the angular topo-cluster widths,
computed as the standard deviation of the displacements of
the topo-cluster’s constituent cells in η and φ with respect
to the topo-cluster barycentre. This accounts for the
spatial extent of the topo-clusters, which may contain energy
deposits from multiple particles.
The distributions of ση and σφ for single-particle samples
are shown in Fig. 10. The structure seen in these
distribu(a)
(b)
(c)
Fig. 7 The purity ρlcelauds, defined for a selected charged pion as the
fractional contribution of the chosen particle to the total true energy in the
leading topo-cluster, shown for pions with εlcelauds >50%. Distributions are
shown for several ptrue bins and in three |ηtrue| regions. The data are
T
taken from a dijet sample without pile-up with 20 < plead < 500 GeV
T
and the statistical uncertainties on the number of MC simulated events
are shown as a hatched band
ATLAS Simulation
-2.5 -2 -1.5 -1 -0.5 0
0.5
1
Fig. 8 The track reconstruction efficiency for charged pions after
applying the tight quality selection criteria to the tracks. Subfigure
(a) shows the efficiency for 1–2 GeV, 2–5 GeV and 5–10 GeV
particles as a function of η, while (b) shows the track reconstruction
efficiency as a function of pT in three |η| bins. A simulated dijet sample
is used, with similar pile-up to that in the 2012 data, and for which
20 < plead < 1000 GeV. The statistical uncertainties in the number of
T
MC simulated events are shown in a darker shading
4 6 8 10
ptrk-ptrue [GeV]
T T
-10 -8
-6
-4
-2
0
2
-10 -8
-6
-4
-2
0
2
Nominal reconstruction
After hit requirements
Fig. 9 The difference between the reconstructed pT of the track from
a charged pion and the particle’s true pT for two bins in truth particle pT
and |η|, determined in dijet MC simulation with similar pile-up to that
in the 2012 data. The shaded bands represent the statistical uncertainty.
The tails in the residuals are substantially diminished upon the
applications is related to the calorimeter geometry. Each
calorimeter layer has a different cell granularity in both dimensions,
and this sets the minimum topo-cluster size. In particular,
the granularity is significantly finer in the electromagnetic
calorimeter, thus particles that primarily deposit their energy
in either the electromagnetic and hadronic calorimeters form
distinct populations. High-energy showers typically spread
over more cells, broadening the corresponding topo-clusters.
If the computed value of ση or σφ is smaller than 0.05, it is
set to 0.05.
A preliminary selection of topo-clusters to be matched to
the tracks is performed by requiring that E clus/ ptrk > 0.1,
4 6 8 10
ptrk-ptrue [GeV]
T T
(b) 5 < ptrue < 10 GeV,
T
2.0 < |ηtrue | < 2.5.
tion of the more stringent silicon detector hit requirements. A simulated
dijet sample with 20 < plead < 1000 GeV is used, and the statistical
T
uncertainties in the number of MC simulated events are shown as a
hatched band
where E clus is the energy of the topo-cluster and ptrk is the
track momentum. The distribution of E clus/ ptrk for the
topocluster with at least 90% of the true energy from the particle
matched to the track – the “correct” one to match to – and for
the closest other topo-cluster in R is shown in Fig. 11. For
very soft particles, it is common that the closest other
topocluster carries E clus/ ptrk comparable to (although smaller
than) the correct topo-cluster. About 10% of incorrect
topoclusters are rejected by the E clus/ ptrk cut for particles with
1 < pT < 2 GeV. The difference in E clus/ ptrk becomes
much more pronounced for particles with pT > 5 GeV,
for which there is a very clear separation between the
corFig. 10 The distribution of ση and σφ , for charged pions, in three
different regions of the detector for three particle pT ranges. The data are
taken from a dijet sample without pile-up with 20 < plead < 500 GeV
T
rect and incorrect topo-cluster matches, resulting in a 30–
40% rejection rate for the incorrect topo-clusters. This is
because at lower pT clusters come from both signal and
electronic or pile-up noise. Furthermore, the particle pT
spectrum is peaked towards lower values, and thus higher- pT
topo-clusters are rarer. The E clus/ ptrk > 0.1 requirement
rejects the correct cluster for far less than 1% of particles.
Next, an attempt is made to match the track to one of
the preselected topo-clusters using the distance metric R
defined in Eq. 5. The distribution of R between the track
and the topo-cluster with > 90% of the truth particle energy
and to the closest other preselected topo-cluster is shown
in Fig. 12 for the dijet MC sample. From this figure, it is
seen that the correct topo-cluster almost always lies at a
small R relative to other clusters. Hence, the closest
preselected topo-cluster in R is taken to be the matched
topocluster. This criterion selects the correct topo-cluster with a
high probability, succeeding for virtually all particles with
pT > 5 GeV. If no preselected topo-cluster is found in a
cone of size R = 1.64, it is assumed that this particle did
not form a topo-cluster in the calorimeter. In such cases the
track is retained in the list of tracks and no subtraction is
performed. The numerical value corresponds to a one-sided
Gaussian confidence interval of 95%, and has not been
optimised. However, as seen in Fig. 12, this cone size almost
and the statistical uncertainties on the number of MC simulated events
are shown as a hatched band
always includes the correct topo-cluster, while rejecting the
bulk of incorrect clusters.
6.4 Evaluation of the expected deposited particle energy
through Ercelfus/ prtrekf determination
It is necessary to know how much energy a particle with
measured momentum ptrk deposits on average, given by
Edep = ptrk Ercelfus/ prtrekf , in order to correctly subtract
the energy from the calorimeter for a particle whose track
has been reconstructed. The expectation value Ercelfus/ prtrekf
(which is also a measure of the mean response) is determined
using single-particle samples without pile-up by summing
the energies of topo-clusters in a R cone of size 0.4 around
the track position, extrapolated to the second layer of the EM
calorimeter. This cone size is large enough to entirely capture
the energy of the majority of particle showers. This is also
sufficient in dijet events, as demonstrated in Fig. 13, where
one might expect the clusters to be broader due to the
presence of other particles. The subscript ‘ref’ is used here and in
the following to indicate E clus/ ptrk values determined from
single-pion samples.
Variations in Ercelfus/ prtrekf due to detector geometry and
shower development are captured by binning the
measurement in the pT and η of the track as well as the layer of
Fig. 11 The distributions of E clus/ ptrk for the topo-cluster with >
90% of the true energy of the particle and the closest other topo-cluster
in R . The data are taken from a dijet sample without pile-up with
20 < plead < 500 GeV and the statistical uncertainties on the number
T
highest energy density (LHED), defined in the next section.
The LHED is also used to determine the order in which cells
are subtracted in subsequent stages of the algorithm.
The spread of the expected energy deposition, denoted by
σ (Edep), is determined from the standard deviation of the
Ercelfus/ prtrekf distribution in single-pion samples. It is used in
order to quantify the consistency of the measured E clus/ ptrk
with the expectation from Ercelfus/ prtrekf in both the
splitshower recovery (Sect. 6.5) and remnant removal (Sect. 6.7).
6.4.1 Layer of highest energy density
The dense electromagnetic shower core has a well-defined
ellipsoidal shape in η–φ. It is therefore desirable to locate this
core, such that the energy subtraction may be performed first
in this region before progressing to the less regular shower
periphery. The LHED is taken to be the layer which shows
the largest rate of increase in energy density, as a function of
the number of interaction lengths from the front face of the
calorimeter. This is determined as follows:
• The energy density is calculated for the j th cell in the i th
layer of the calorimeter as
of MC simulated events are shown as a hatched band. A track is only
used for energy subtraction if a topo-cluster is found inside a cone of
R = 1.64 for which E clus/ ptrk > 0.1, as indicated by the vertical
dashed line
ρi j =
Ei j
Vi j
GeV/ X03 ,
(6)
with Ei j being the energy in and Vi j the volume of the cell
expressed in radiation lengths. The energy measured in
the Presampler is added to that of the first layer in the EM
calorimeter. In addition, the Tile and HEC calorimeters
are treated as single layers. Thus, the procedure takes
into account four layers – three in the EM calorimeter
and one in the hadronic calorimeter. Only cells in the
topo-clusters matched to the track under consideration
are used.
• Cells are then weighted based on their proximity to the
extrapolated track position in the layer, favouring cells
that are closer to the track and hence more likely to
contain energy from the selected particle. The weight for
each cell, wi j , is computed from the integral over the
cell area in η–φ of a Gaussian distribution centred on the
extrapolated track position with a width in R of 0.035,
similar to the Molière radius of the LAr calorimeter.
• A weighted average energy density for each layer is
calculated as
Fig. 12 The distributions of R for the topo-cluster with > 90% of
the true energy of the particle and the closest other topo-cluster, both
satisfying E clus/ ptrk > 0.1. The data are taken from a dijet sample
without pile-up with 20 < plead < 500 GeV and the statistical
uncerT
tainties on the number of MC simulated events are shown as a hatched
band. A track is only used for energy subtraction if a topo-cluster is
found with E clus/ ptrk > 0.1 inside a cone of R < 1.64, as indicated
by the vertical dashed line
Fig. 13 The cone size R around the extrapolated track required to
encompass both the leading and sub-leading topo-clusters, for π ± when
< 70% of their true deposited energy in topo-clusters is contained in the
leading topo-cluster, but > 90% of the energy is contained in the two
leading topo-clusters. The data are taken from a dijet sample without
pile-up with 20 < plead < 500 GeV and the statistical uncertainties on
T
the number of MC simulated events are shown as a hatched band
(a)
ρ i =
wi j ρi j .
j
• Finally, the rate of increase in ρ i in each layer is
determined. Taking di to be the depth of layer i in interaction
lengths, the rate of increase is defined as
ρi =
ρ i −
di − di−1
ρ i−1 ,
(8)
where the values ρ 0 = 0 and d0 = 0 are assigned, and
the first calorimeter layer has the index i = 1.
The layer for which
ρ is maximal is identified as the LHED.
Fig. 14 The significance of the difference between the energy of the
matched topo-cluster and the expected deposited energy Edep and
that of the matched topo-cluster, for π ± when < 70% and > 90% of
the true deposited energy in topo-clusters is contained in the matched
topo-cluster for different ptrue and |ηtrue| ranges. The vertical line
indi
T
cates the value below which additional topo-clusters are matched to the
track for cell subtraction. Subfigures a–f indicate that a single cluster is
6.5 Recovering split showers
Particles do not always deposit all their energy in a single
topo-cluster, as seen in Fig. 5. Clearly, handling the multiple
topo-cluster case is crucial, particularly the two topo-cluster
case, which is very common. The next stages of the
algorithm are therefore firstly to determine if the shower is split
across several clusters, and then to add further clusters for
consideration when this is the case.
The discriminant used to distinguish the single and
multiple topo-cluster cases is the significance of the difference
between the expected energy and that of the matched
topocluster (defined using the algorithm in Sect. 6.3),
S(E clus) =
E clus −
σ (Edep)
Edep
.
The distribution of S(E clus) is shown in Fig. 14 for two
categories of matched topo-clusters: those with εiclus > 90%
considered (93, 95, 95, 94, 95, 91) % of the time when εmcluatsched > 90%;
while additional topo-clusters are considered (49, 39, 46, 56, 52, 60) %
of the time when εmcluatsched < 70%. The data are taken from a dijet sample
without pile-up with 20 < plead < 500 GeV and the statistical
uncer
T
tainties on the number of MC simulated events are shown as a hatched
band
and those with εiclus < 70%. A clear difference is observed
between the S(E clus) distributions for the two categories,
demonstrating the separation between showers that are and
are not contained in a single cluster. More than 90% of
clusters with εiclus > 90% have S(E clus) > −1. Based on
this observation a split shower recovery procedure is run if
S(E clus) < −1: topo-clusters within a cone of R = 0.2
around the track position extrapolated to the second EM
calorimeter layer are considered to be matched to the track.
As can be seen in the figure, the split shower recovery
procedure is typically run 50% of the time when εmcluatsched < 70%.
The full set of matched clusters is then considered when the
energy is subtracted from the calorimeter.
(9)
6.6 Cell-by-cell subtraction
Once a set of topo-clusters corresponding to the track has
been selected, the subtraction step is executed. If Edep
exceeds the total energy of the set of matched topo-clusters,
π
π
π
π
π
π
Fig. 15 An idealised example of how the cell-by-cell subtraction
works. Cells in two adjacent calorimeter layers (EMB2 and EMB3)
are shown in grey if they are not in clusters, red if they belong to a
π + cluster and in green if contributed by a π 0 meson. Rings are placed
around the extrapolated track (represented by a star) and then the cells
in these are removed ring by ring starting with the centre of the shower
then the topo-clusters are simply removed. Otherwise,
subtraction is performed cell by cell.
Starting from the extrapolated track position in the LHED,
a parameterised shower shape is used to map out the most
likely energy density profile in each layer. This profile is
determined from a single π ± MC sample and is dependent
on the track momentum and pseudorapidity, as well as on
the LHED for the set of considered topo-clusters. Rings are
formed in η–φ space around the extrapolated track. The rings
are just wide enough to always contain at least one
calorimeter cell, independently of the extrapolated position, and are
confined to a single calorimeter layer. Rings within a single
layer are equally spaced in radius. The average energy
density in each ring is then computed, and the rings are ranked
in descending order of energy density, irrespective of which
layer each ring is in. Subtraction starts from the ring with
the highest energy density (the innermost ring of the LHED)
and proceeds successively to the lower-density rings. If the
(a), where the expected energy density is highest and moving outwards,
and between layers. This sequence of ring subtraction is shown in
subfigures (a) through (g). The final ring contains more energy than the
expected energy, hence this is only partially subtracted (g), indicated
by a lighter shading
energy in the cells in the current ring is less than the
remaining energy required to reach Edep , these cells are simply
removed and the energy still to be subtracted is reduced by
the total energy of the ring. If instead the ring has more energy
than is still to be removed, each cell in the ring is scaled down
in energy by the fraction needed to reach the expected energy
from the particle, then the process halts. Figure 15 shows a
cartoon of how this subtraction works, removing cells in
different rings from different layers until the expected energy
deposit is reached.
6.7 Remnant removal
If the energy remaining in the set of cells and/or topo-clusters
that survive the energy subtraction is consistent with the
width of the Ercelfus/ prtrekf distribution, specifically if this energy
is less than 1.5σ (Edep), it is assumed that the topo-cluster
system was produced by a single particle. The remnant energy
Fig. 16 The significance of the difference between the energy of the
matched topo-cluster and the expected deposited energy Edep for
π ± with either < 70% or > 90% of the total true energy in the
matched topo-cluster originating from the π ± for different ptrue and
T
|ηtrue| ranges. The vertical line indicates the value below which the
remnant topo-cluster is removed, as it is assumed that in this case
no other particles contribute to the topo-cluster. Subfigures a–f
inditherefore originates purely from shower fluctuations and so
the energy in the remaining cells is removed. Conversely,
if the remaining energy is above this threshold, the remnant
topo-cluster(s) are retained – it being likely that multiple
particles deposited energy in the vicinity. Figure 16 shows how
this criterion is able to separate cases where the matched
topocluster has true deposited energy only from a single particle
from those where there are multiple contributing particles.
After this final step, the set of selected tracks and the
remaining topo-clusters in the calorimeter together should
ideally represent the reconstructed event with no double
counting of energy between the subdetectors.
7 Performance of the subtraction algorithm at truth level
The performance of each step of the particle flow algorithm is
evaluated exploiting the detailed energy information at truth
cate that when ρmclautsched > 90% the remnant is successfully removed
(91, 89, 94, 89, 91, 88) % of the time; while when ρmclautsched < 70% the
remnant is retained (81, 80, 76, 84, 83, 91) % of the time. The data are
taken from a dijet sample without pile-up with 20 < plead < 500 GeV
T
and the statistical uncertainties on the number of MC simulated events
are shown as a hatched band
level available in Monte Carlo generated events. For these
studies a dijet sample with leading truth jet pT between 20
and 500 GeV without pile-up is used.
7.1 Track–cluster matching performance
Initially, the algorithm attempts to match the track to a
single topo-cluster containing the full particle energy.
Figure 17 shows the fraction of tracks whose matched cluster
has εlcelauds > 90% or εlcelauds > 50%. When almost all of the
deposited energy is contained within a single topo-cluster,
the probability to match a track to this topo-cluster (matching
probability) is above 90% in all η regions, for particles with
pT > 2 GeV. The matching probability falls to between 70
and 90% when up to half the particle’s energy is permitted to
fall in other topo-clusters. Due to changes in the calorimeter
geometry, the splitting rate and hence the matching
probability vary significantly for particles in different
pseudorapidity regions. In particular, the larger cell size at higher |η|
from a dijet sample without pile-up with 20 < plead < 500 GeV and
T
the statistical uncertainties on the number of MC simulated events are
shown as a hatched band
(a)
(b)
(c)
Fig. 18 The fraction of the true energy of a given particle contained
within the initially matched topo-cluster for particles where the split
shower recovery procedure is run (SSR run) and where it is not (No
SSR). For cases where most of the energy is contained in the initially
matched topo-cluster the procedure is less likely to be run. The data are
taken from a dijet sample without pile-up with 20 < plead < 500 GeV
T
and the statistical uncertainties on the number of MC simulated events
are shown as a hatched band
enhances the likelihood of capturing soft particle showers in
a single topo-cluster, as seen in Figs. 4 and 5, which results
in the matching efficiency increasing at low pT for |η| > 2.
7.2 Split-shower recovery performance
Frequently, a particle’s energy is not completely contained
within the single best-match topo-cluster, in which case the
split shower recovery procedure is applied. The effectiveness
of the recovery can be judged based on whether the procedure
is correctly triggered, and on the extent to which the energy
subtraction is improved by its execution.
Figure 18 shows the fraction εmcluatsched of the true deposited
energy contained within the matched topo-cluster, separately
for cases where the split shower recovery procedure is and
is not triggered, as determined by the criteria described in
Sect. 6.5. In the cases where the split shower recovery
procedure is not run, εmcluatsched is found to be high, confirming
that the comparison of topo-cluster energy and Ercelfus/ prtrekf
is successfully identifying good topo-cluster matches.
Conversely, the split shower recovery procedure is activated when
εmcluatsched is low, particularly for higher- pT particles, which are
expected to split their energy between multiple topo-clusters
more often. Furthermore, as the particle pT rises, the width
of the calorimeter response distribution decreases, making it
easier to distinguish the different cases.
Figure 19 shows the fraction fsculbus of the true deposited
energy of the pions considered for subtraction, in the set of
clusters matched to the track, as a function of true pT. For
particles with pT > 20 GeV, with split shower recovery
active, fsculbus is greater than 90% on average. The subtraction
algorithm misses more energy for softer showers, which are
ATLAS Simulation
s = 8 TeV
5
10
15
20
25
Fig. 19 The fraction of the true energy of a given particle considered
in the subtraction procedure f clus after the inclusion of the split shower
sub
recovery algorithm. The data are taken from a dijet sample without
pileup with 20 < plead < 500 GeV and the statistical uncertainties on the
T
number of MC simulated events are shown as a hatched band
harder to capture completely. While fsculbus could be increased
by simply attempting recovery more frequently, expanding
the topo-cluster matching procedure in this fashion increases
the risk of incorrectly subtracting neutral energy; hence the
split shower recovery procedure cannot be applied
indiscriminately. The settings used in the studies presented in this paper
are a reasonable compromise between these two cases.
7.3 Accuracy of cell subtraction
The cell subtraction procedure removes the expected
calorimeter energy contribution based on the track properties. It is
instructive to identify the energy that is incorrectly subtracted
from the calorimeter, to properly understand and optimise the
performance of the algorithm.
Truth particles are assigned reconstructed energy in
topoclusters as described in Sect. 3.2, and then classified
depending on whether or not a track was reconstructed for the
particle. The reconstructed energy assigned to each
particle is computed both before subtraction and after the
subtraction has been performed, using the remaining cells.
In the ideal case, the subtraction should remove all the
energy in the calorimeter assigned to stable truth particles
which have reconstructed tracks, and should not remove
any energy assigned to other particles. The total transverse
momentum of clusters associated with particles in a truth
jet where a track was reconstructed before (after)
subtraction is defined as pT±,pre−sub( pT±,post−sub). Similarly, the
transverse momentum of clusters associated with the other
particles in a truth jet, neutral particles and those that did not
create selected, reconstructed tracks, before (after)
subtrac(10)
(11)
(12)
tion as pT0,pre−sub( pT0,post−sub). The corresponding transverse
momentum fractions are defined as f ± = pT±,pre−sub/ pTjet,true
( f 0 = pT0,pre−sub/ pTjet,true).
Three measures are established, to quantify the degree to
which the energy is incorrectly subtracted. The incorrectly
subtracted fractions for the two classes of particles are:
such that R± corresponds to the fraction of surviving
momentum associated with particles where the track measurement
is used, which should have been removed, while R0 gives
the fraction of momentum removed that should have been
retained as it is associated with particles where the
calorimeter measurement is being used. These two variables are
combined into the confusion term
C = R± − R0,
which is equivalent to the net effect of both mistakes on
the final jet transverse momentum, as there is a potential
cancellation between the two effects. An ideal subtraction
algorithm would give zero for all three quantities.
Figure 20 shows the fractions associated with the different
classes of particle, before and after the subtraction algorithm
has been executed for jets with a true energy in the range 40–
60 GeV. The confusion term is also shown, multiplied by the
jet energy scale factor that would be applied to these
reconstructed jets, such that its magnitude (C × JES) is directly
comparable to the reconstructed jet resolution.
Clearly, the subtraction does not perform perfectly, but
most of the correct energy is removed – the mean value of
the confusion is −1%, with an RMS of 7.6%. The slight
bias towards negative values suggests that the subtraction
algorithm is more likely to remove additional neutral energy
rather than to miss charged energy and the RMS gives an
indication of the contribution from this confusion to the overall
jet resolution.
Figure 21 shows C × JES as a function of pT. The
mean value of the JES weighted confusion remains close
to zero and always within ±1.5%, showing that on
average the algorithm removes the correct amount of energy
from the calorimeter. The RMS decreases with increasing
pT. This is due to a combination of the particle pT
spectrum becoming harder, such that the efficiency of
matching to the correct cluster increases; the increasing difficulty
0.06
Fig. 20 The fractions of the jet calorimeter energy that have been
incorrectly subtracted by the cell subtraction algorithm, for jets with
40 < pTtrue < 60 GeV and |η| < 1.0 in dijet MC simulation without
pile-up. The statistical uncertainty is indicated by the hatched bands.
Subfigure (a) shows the fraction of jet transverse momentum carried
by reconstructed tracks before subtraction f ± (hashed) and the
corresponding fraction after subtraction R± (solid); b shows the fraction
of jet transverse momentum carried by particles without reconstructed
tracks before subtraction f 0 (hashed) and the corresponding fraction
after subtraction R0 (solid); and c shows the confusion C = R± − R0,
scaled up by the jet energy scale, derived as discussed in Sect. 8
)
S
JE0.08 ATLAS Simulation
x
(C0.06
μ0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
Particle Flow Jets
|η|<1.0, 〈μ〉 = 0
Particle Flow Jets
|η|<1.0, 〈μ〉 = 0
)
S
JE0.18 ATLAS Simulation
xC0.16
(
SM0.14
R0.12
Fig. 21 As a function of the jet pT, subfigure a shows the mean of the
confusion term C = R± − R0, scaled up by the jet energy scale, derived
as discussed in Sect. 8, and (b) shows the RMS of this distribution. The
of subtracting the hadronic showers in the denser
environments of high- pT jets; and the fact that no subtraction is
performed for tracks above 40 GeV, resulting in the fraction of
the jet considered for subtraction decreasing with increasing
jet pT.
7.4 Visualising the subtraction
For a concrete demonstration of successes and failures of the
subtraction algorithm, it is instructive to look at a specific
event in the calorimeter. Figure 22 illustrates the action of the
algorithm in the second layer of the EM calorimeter, where
the majority of low-energy showers are contained. The focus
is on a region where a 30 GeV truth jet is present. In general,
the subtraction works well in the absence of pile-up, as the
error bars denote the statistical uncertainty. The MC samples used do
not include pile-up
two topo-clusters inside the jet radius with energy mainly
associated with charged particles at truth level are entirely
removed. Nevertheless, examples can be seen where small
mistakes are made. For example, the algorithm additionally
removes some cells containing neutral-particle energy from
the topo-cluster just above the track at (η, φ) = (0.0, 1.8).
The figure also shows the same event, overlaid with pile-up
corresponding to μ = 40. Pile-up contributions are
identified by subtracting the energy reconstructed without pile-up
and are illustrated in blue. The pile-up supplies many more
energy deposits and tracks within the region under scrutiny.
However, the subtraction continues to function effectively,
removing energy in the vicinity of pile-up tracks and hence
the post-subtraction cell distribution more closely
resembles that without pile-up, especially inside the jet radius.
〉
t
en10-1
v
E
/
2
.
0
/
ts10-2
e
J
e
k
a
F
〈
10-3
〈μ〉 ~ 24
〈μ〉 ~ 24
Fig. 29 In the presence of pile-up, ‘fake jets’ can arise from particles
not produced in the hard-scatter interaction. Subfigure a shows the
number of fake jets (jets not matched to truth jets with pT > 4 GeV within
R < 0.4) and b the efficiency of reconstructing a hard-scatter jet
of jet resolution from pile-up and eliminates jets
reconstructed from pile-up deposits, making the particle flow
method a powerful tool, especially as the LHC luminosity
increases.
10.1 Pile-up jet rate
In the presence of pile-up, jets can arise from particles not
produced in the hard-scatter interaction. These jets are here
referred to as ‘fake jets’. Figure 29a shows the fake-jet
rate as a function of the jet η for particle flow jets
compared to calorimeter jets with and without track-based
pileup suppression [
65
]. These rates are evaluated using a dijet
MC sample overlaid with simulated minimum-bias events
approximating the data-taking conditions in 2012. The jet
vertex fraction (JVF) is defined as the ratio of two scalar
sums of track momenta: the numerator is the scalar sum of
the pT of tracks that originate from the hard-scatter primary
vertex and are associated with the jet; the denominator is the
scalar sum of the transverse momenta of all tracks associated
with that jet.4 Within the tracker coverage of |η| < 2.5, the
fake rate for particle flow jets drops by an order of magnitude
compared to the standard calorimeter jets. The small increase
in the rate of particle flow fake jets around 1.0 < |η| < 1.2
is related to the worse performance of the particle flow
algorithm in the transition region between the barrel and extended
barrel of the Tile calorimeter, which is significantly affected
by pile-up contributions [
3
].
4 Jets with no tracks associated with them are assigned JVF = −1.
(reconstructed jet found within R < 0.4 with pT > 15 GeV) in dijet
MC events. Simulated pile-up conditions are similar to the data-taking
in 2012
For |η| > 2.5, the jets are virtually identical, and hence
the fake rate shows no differences. This rejection rate is
comparable to that achieved using the JVF discriminant, which
can likewise only be applied within the tracker coverage.
Here, the comparison is made to a |JVF| threshold of 0.25 for
calorimeter jets, which is not as powerful as the particle flow
fake-jet rate reduction. The inefficiency of the particle flow
jet-finding is negligible, as can be seen from Fig. 29b. In
contrast, the inefficiency generated by requiring |JVF| > 0.25
is clearly visible (it should be noted that in 2012 JVF cuts
were only applied to calorimeter jets up to a pT of 50 GeV).
Below 30 GeV, the jet resolution causes some reconstructed
jets to fall below the jet reconstruction energy threshold so
these values are not shown.
A more detailed study of the pile-up jet rates is carried
out in a Z → μμ sample, both in data and MC simulation,
by isolating several phase-space regions that are enriched in
hard-scatter or pile-up jets. A preselection is made using the
criteria described in Sect. 4. The particle flow algorithm is
run on these events and further requirements are applied:
events are selected with two isolated muons, each with
pT > 25 GeV, with invariant mass 80 < mμμ < 100 GeV
and pμμ > 32 GeV, ensuring that the boson recoils against
T
hadronic activity. Figure 30 displays two regions of phase
space: one opposite the recoiling boson, where large amounts
of hard-scatter jet activity are expected, and one off-axis,
which is more sensitive to pile-up jet activity.
Figure 31 shows the average number of jets with pT >
20 GeV in the hard-scatter-enriched region for different |η|
ranges as a function of the number of primary vertices. The
distributions are stable for particle flow jets and for
calorimeter jets with JVF > 0.25 as a function the number of
pri| |
mary vertices in all η regions. The only exception is in the
| |
Fig. 30 A diagram displaying the regions of r –φ phase space which
are expected to be dominated by hard-scatter jets (opposite in the r –φ
pile-up jet activity (perpendicular to the Z → μμ decay)
plane to the Z μμ decay) and where there is greater sensitivity to
→
the jet fake rate is visible for jet pseudorapidities very close
to the tracker boundary. This is due to the jet area collecting
charged-particle pile-up contributions that are outside the ID
acceptance. If the JVF cut is not applied to the calorimeter
jets, the jet multiplicity grows with increasing pile-up.
Figure 32 shows that in the pile-up-enriched selection, the
particle flow and calorimeter jets with a JVF selection still show
no dependence on the number of reconstructed vertices in all
η regions. The observed difference between data and MC
| |
simulation for both jet collections is due to a poor modelling
of this region of phase space. These distributions establish
the high stability of particle flow jets in varying pile-up
conditions.
10.2 Pile-up effects on jet energy resolution
In addition to simply suppressing jets from pile-up, the
particle flow procedure reduces the fluctuations in the jet energy
Number of Primary Vertices
Number of Primary Vertices
Number of Primary Vertices
〉0.14
s
t
e
J
f
.o0.13
o
N
〈
0.3
0.2
0.1
(a)
(a)
〉s 0.5
t
N
〈0.44
Fig. 31 The average number of jets per event, for jets with pT >
20 GeV, as a function of the number of primary vertices in the Z
samples. The distributions are shown in three different |η| regions for
particle flow jets, calorimeter jets and calorimeter jets with an additional
→ μμ
cut on JVF. The jets are selected in a region of φ opposite the Z boson’s
direction,
φ (Z , jet) > 3π/4, which is enriched in hard-scatter jets.
The statistical uncertainties in the number of events are shown as a
hatched band
ATLAS
Number of Primary Vertices
Number of Primary Vertices
Number of Primary Vertices
Fig. 32 The average number of jets per event, for jets with pT >
20 GeV, as a function of the number of primary vertices in the Z
samples. The distributions are shown in three different |η| regions for
particle flow jets, calorimeter jets and calorimeter jets with an additional
→ μμ
cut on JVF. The jets are selected in a region of φ perpendicular to the
Z boson’s direction, π/4 <
φ (Z , jet) < 3π/4, which is enriched
in pile-up jets. The statistical uncertainties in the number of events are
shown as a hatched band
R
/R
σ 0.3
0.25
Fig. 33 The resolutions of calorimeter and particle flow jets
determined as a function of pT in MC dijet simulation, compared with no
pile-up and conditions similar to those in the 2012 data. The quadratic
difference in the resolution with and without pile-up is shown in
the lower panel for LC + JES (blue) and particle flow (black) jets.
The data are taken from dijet samples, with and without pileup, with
20 < plead < 500 GeV and the statistical uncertainties on the number
T
of MC simulated events are shown
measurements due to pile-up contributions. This is
demonstrated by Fig. 33, which compares the jet energy resolution
for particle flow and calorimeter jets with and without
pileup. Even in the absence of pile-up, the particle flow jets have
a better resolution at pT values below 50 GeV. With pile-up
conditions similar to those in the 2012 data, the cross-over
point is at pT = 90 GeV, indicating that particle flow
reconstruction alleviates a significant contribution from pile-up
even for fairly energetic jets. The direct effect of pile-up can
be seen in the lower panel, where the difference in quadrature
between the resolutions with and without pile-up is shown.
The origin of the increase in the resolution with pile-up is
discussed in detail in Ref. [
6
]. It is shown that additional
energy deposits are the primary cause of the degradation
of the calorimeter jet resolution. This effect is mitigated by
the particle flow algorithm in two ways. Firstly, the
subtraction of topo-clusters formed by charged particles from
pileup vertices prior to jet-finding eliminates a major source of
fluctuations. Secondly, the increase in the constituent scale
of hard-scatter jets from the use of calibrated tracks, rather
than energy clusters in the calorimeter, amplifies the
signal, effectively suppressing the contribution from pile-up.
This second mechanism is found to be the main contributing
factor.
For 40 GeV jets, the total jet resolution without pile-up
is 10%. Referring back to Fig. 20c, confusion contributes
∼ 8% to the jet resolution in the absence of pile-up. Since
the terms are combined in quadrature, confusion contributes
significantly to the overall jet resolution, although it does not
totally dominate. While additional confusion can be caused
by the presence of pile-up particles, the net effect is that
pileup affects the resolution of particle flow jets less than that of
calorimeter jets.
11 Comparison of data and Monte Carlo simulation
It is crucial that the quantities used by the particle flow
reconstruction are accurately described by the ATLAS detector
simulation. In this section, particle flow jet properties are
compared for Z → μμ and t t¯ events in data and MC
simulation. Various observables are validated, from low-level
jet characteristics to derived observables relevant to physics
analyses.
11.1 Individual jet properties
A sample of jets is selected in Z → μμ events, as in Sect. 8,
and used for a comparison between data and MC simulation.
As the subtraction takes place at the cell level, the energy
subtracted from each layer of the calorimeter demonstrates
how well the subtraction procedure is modelled. To
determine the energy before subtraction the particle flow jets are
matched to jets formed solely from topo-clusters at the
electromagnetic scale. A similar selection to that used to evaluate
the jet energy scale is used. The leading jet is required to be
opposite a reconstructed Z boson decaying to two muons
with φ > π − 0.4. The pT of the reconstructed boson is
required to be above 32 GeV and the reconstructed jets must
have 40 < pT < 60 GeV. Figures 34 and 35 show the
properties of central jets. The MC simulation describes the data
reasonably well for the jet track multiplicity, fraction of the
jet pT carried by tracks as well as the amount of subtracted or
surviving energy in each layer of the EM barrel. Similar
levels of agreement are observed for jets in the endcap regions
of the detector.
11.2 Event-level observables
Finally, the particle flow performance is examined in a
sample of selected t t¯ events; a sample triggered by a single-muon
trigger with a single offline reconstructed muon is used. At
least four jets with pT > 25 GeV and |η| < 2.0 are required
and two of these are required to have been b-tagged using the
MV1 algorithm and have pT > 35 and 30 GeV.5 This selects
5 As the b-tagging algorithm has only been calibrated for calorimeter
jets, the particle flow jets use the calorimeter jet information from the
closest jet in R in order to decide if the jet is b-tagged.
weighted by the track pT and normalised to the number of jets,
illustrating the transverse momentum flow from particles of different pT. The
distribution is shown both for tracks satisfying the hard-scatter primary
vertex association criteria and forming the jet as well as the additional
tracks within R = 0.4 of the jet failing to satisfy the hard-scatter
primary vertex association criteria. The darker shaded bands represent
the statistical uncertainties
a 95% pure sample of t t¯ events. The event E miss is
recon
T
structed from the vector sum of the calibrated jets with pT >
20 GeV, the muon and all remaining tracks associated with
the hard-scatter primary vertex but not associated with these
objects. This is then used to form the transverse mass
variable defined by mT = 2 pTμ ETmiss(1 − cos( φ (μ, ETmiss))).
The invariant mass of the two leading non-b-tagged jets, mjj,
forms a hadronic W candidate, while the invariant masses of
each of the two b-tagged jets and these two non-b-tagged jets
form two hadronic top quark candidates, mjjb.
Figure 36 compares the data with MC simulation for
these three variables; mT, mjj and mjjb. The MC
simulation describes the data very well in all three
distributions. Figure 37 shows the mjj distribution for particle
flow jets compared to the distribution obtained from the
same selection applied to calorimeter jets (with |JVF| >
Page 30 of 47
Fig. 35 Comparison of the fractions of jet energy removed from a
single layer of the electromagnetic calorimeter relative to the total energy
of the constituents of the matched calorimeter jet E Ccoanlostit. (left) and
retained relative to the total energy of the constituents of the particle
flow jet E constit. (right) by the cell subtraction algorithm in different
lay
Pflow
ers of the EM barrel, for a selection of jets with 40 < pT < 60 GeV and
|η| < 0.6, selected in Z → μμ events from collision data and MC
simulation. The simulated samples are normalised to the number of events
in data. The darker shaded bands represent the statistical uncertainties
500
C 2
/taaM10..551
D
20
ATLAS
Particle Flow
Data s = 8 TeV, 20.2 fb-1
Total SM prediction
tt→ ql,ll
Single Top
60 < mjj < 100 GeV
Data s = 8 TeV, 20.2 fb-1
Total SM prediction
tt→ ql,ll
Single Top
mT > 45 GeV
ATLAS
Particle Flow
V
e
G2500
4
/
ts2000
n
e
vE1500
1000
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C 2
/taaM10..551
D
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40
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G Particle Flow
43000
/
ts2500
n
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v2000
E
1500
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C 2
t/aaM01..551
D
Data s = 8 TeV, 20.2 fb-1
Total SM prediction
tt→ ql,ll
Single Top
60 < mjj < 100 GeV
mT > 45 GeV
100
150
200
250
300 350
mjjb [GeV]
0.25). For the calorimeter jet selection, the E miss is
recon
T
structed from the muon, jets, photons and remaining
unassociated clusters [
53
]. The two selections are applied
separately; hence the exact numbers of events in the plots
differ. The particle flow reconstruction provides a good
measure and narrower width of the peak for both low and
high pTjj. Gaussian fits to the data in the range 65 <
mjj < 95 GeV give widths of (13.8 ± 0.4) GeV and
(16.2 ± 0.6) GeV for particle flow reconstruction and
that based on calorimeter jets, respectively, for pTjj <
80 GeV. For pTjj > 80 GeV, the widths were found to be
(11.2 ± 0.2) GeV and (11.9 ± 0.3) GeV, respectively. At
very high values of pTW , the gains would further diminish
(see Fig. 26).
12 Conclusions
The particle flow algorithm used by the ATLAS
Collaboration for 20.2 fb−1 of pp collisions at 8 TeV at the LHC is
presented. This algorithm aims to accurately subtract energy
deposited by tracks in the calorimeter, exploiting the good
calorimeter granularity and longitudinal segmentation. Use
of particle flow leads to improved energy and angular
resolution of jets compared to techniques that only use the
calorimeter in the central region of the detector.
In 2012 data-taking conditions, the transverse
momentum resolution of particle flow jets calibrated with a global
sequential correction is superior up to pT ∼ 90 GeV for
|η| < 1.0. For a representative jet ptrue of 30 GeV, the
reso
T
Page 32 of 47
V2400 ATLAS
e
G2200
/42000
ts1800
n
e1600
v
E1400
1200
1000
800
600
400
200
Data, s = 8 TeV, 20.2 fb-1
LC+JES Jets
pjj < 80 GeV
T
V2400 ATLAS
e
G2200
/42000
ts1800
n
e1600
v
E1400
1200
1000
800
600
400
200
Data, s = 8 TeV, 20.2 fb-1
LC+JES Jets
pjj > 80 GeV
T
20
40
60
80
100 120 140 160 180
mjj [GeV]
20
40
60
80
(b)
is split into those events where the reconstructed W candidate has pTjj < 80 GeV and pTjj > 80 GeV. The errors shown are purely statistical
lution is improved from the 17.5% resolution of calorimeter
jets with local cluster weighting calibration to 14%. Jet
angular resolutions are improved across the entire pT spectrum,
with σ (η) and σ (φ) decreasing from 0.03 to 0.02 and 0.05
to 0.02, respectively, for a jet pT of 30 GeV.
Rejection of charged particles from pile-up interactions in
jet reconstruction leads to substantially better jet resolution
and to the suppression of jets due to pile-up interactions by
an order of magnitude within the tracker acceptance, with
negligible inefficiency for jets from the hard-scatter
interaction. This outperforms a purely track-based jet pile-up
discriminant typically used in ATLAS analyses, which achieves
similar pile-up suppression at the cost of about one percent
in hard-scatter jet efficiency.
The algorithm therefore achieves a better performance for
hadronic observables such as reconstructed resonant particle
masses.
Studies which compare data with MC simulation
demonstrate that jet properties used for energy measurement and
calibration are modelled well by the ATLAS simulation, both
before and after application of the particle flow algorithm.
This translates to good agreement between data and
simulation for derived physics observables, such as invariant masses
of combinations of jets.
The algorithm has been integrated into the ATLAS
software framework for Run 2 of the LHC. As demonstrated, it
is robust against pile-up and should therefore perform well
under the conditions encountered in Run 2.
Acknowledgements We thank CERN for the very successful
operation of the LHC, as well as the support staff from our institutions
without whom ATLAS could not be operated efficiently. We
acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC,
Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC,
Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada;
CERN; CONICYT, Chile; CAS, MOST and NSFC, China;
COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech
Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DSM/IRFU,
France; SRNSF, Georgia; BMBF, HGF, and MPG, Germany; GSRT,
Greece; RGC, Hong Kong SAR, China; ISF, I-CORE and Benoziyo
Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco;
NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT,
Portugal; MNE/IFA, Romania; MES of Russia and NRC KI,
Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and
MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and
Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern
and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, UK;
DOE and NSF, USA. In addition, individual groups and members have
received support from BCKDF, the Canada Council, CANARIE, CRC,
Compute Canada, FQRNT, and the Ontario Innovation Trust, Canada;
EPLANET, ERC, ERDF, FP7, Horizon 2020 and Marie
SkłodowskaCurie Actions, European Union; Investissements d’Avenir Labex and
Idex, ANR, Région Auvergne and Fondation Partager le Savoir, France;
DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia
programmes co-financed by EU-ESF and the Greek NSRF; BSF, GIF
and Minerva, Israel; BRF, Norway; CERCA Programme Generalitat de
Catalunya, Generalitat Valenciana, Spain; the Royal Society and
Leverhulme Trust, UK. The crucial computing support from all WLCG
partners is acknowledged gratefully, in particular from CERN, the ATLAS
Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway,
Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF
(Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK)
and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG
resource providers. Major contributors of computing resources are listed
in Ref. [
66
].
Open Access This article is distributed under the terms of the Creative
Commons Attribution 4.0 International License (http://creativecomm
ons.org/licenses/by/4.0/), which permits unrestricted use, distribution,
and reproduction in any medium, provided you give appropriate credit
to the original author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made.
Funded by SCOAP3.
Page 34 of 47
ATLAS Collaboration
Page 36 of 47
Page 38 of 47
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G. Watts140, S. Watts87, B. M. Waugh81, A. F. Webb11, S. Webb86, M. S. Weber18, S. W. Weber177, S. A. Weber31,
J. S. Webster6, A. R. Weidberg122, B. Weinert64, J. Weingarten57, C. Weiser51, H. Weits109, P. S. Wells32, T. Wenaus27,
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L. Zwalinski32
1 Department of Physics, University of Adelaide, Adelaide, Australia
2 Physics Department, SUNY Albany, Albany, NY, USA
3 Department of Physics, University of Alberta, Edmonton, AB, Canada
4 (a)Department of Physics, Ankara University, Ankara, Turkey; (b)Istanbul Aydin University, Istanbul, Turkey; (c)Division
of Physics, TOBB University of Economics and Technology, Ankara, Turkey
5 LAPP, CNRS/IN2P3 and Université Savoie Mont Blanc, Annecy-le-Vieux, France
6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA
7 Department of Physics, University of Arizona, Tucson, AZ, USA
8 Department of Physics, The University of Texas at Arlington, Arlington, TX, USA
9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece
10 Physics Department, National Technical University of Athens, Zografou, Greece
11 Department of Physics, The University of Texas at Austin, Austin, TX, USA
12 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan
13 Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain
14 Institute of Physics, University of Belgrade, Belgrade, Serbia
15 Department for Physics and Technology, University of Bergen, Bergen, Norway
16 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA
17 Department of Physics, Humboldt University, Berlin, Germany
18 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern,
Switzerland
19 School of Physics and Astronomy, University of Birmingham, Birmingham, UK
20 (a)Department of Physics, Bogazici University, Istanbul, Turkey; (b)Department of Physics Engineering, Gaziantep
University, Gaziantep, Turkey; (c)Faculty of Engineering and Natural Sciences, Istanbul Bilgi University, Istanbul,
Turkey; (d)Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
21 Centro de Investigaciones, Universidad Antonio Narino, Bogotá, Colombia
22 (a)INFN Sezione di Bologna, Bologna, Italy; (b)Dipartimento di Fisica e Astronomia, Università di Bologna, Bologna,
Italy
23 Physikalisches Institut, University of Bonn, Bonn, Germany
24 Department of Physics, Boston University, Boston, MA, USA
62 (a)Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong; (b)Department of Physics,
The University of Hong Kong, Hong Kong, China; (c)Department of Physics and Institute for Advanced Study, The Hong
Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
63 Department of Physics, National Tsing Hua University, Hsinchu City, Taiwan
64 Department of Physics, Indiana University, Bloomington, IN, USA
65 Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria
66 University of Iowa, Iowa City, IA, USA
67 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA
68 Joint Institute for Nuclear Research, JINR Dubna, Dubna, Russia
69 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan
70 Graduate School of Science, Kobe University, Kobe, Japan
71 Faculty of Science, Kyoto University, Kyoto, Japan
72 Kyoto University of Education, Kyoto, Japan
73 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan
74 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina
75 Physics Department, Lancaster University, Lancaster, UK
76 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy
77 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK
78 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana,
Ljubljana, Slovenia
79 School of Physics and Astronomy, Queen Mary University of London, London, UK
80 Department of Physics, Royal Holloway University of London, Surrey, UK
81 Department of Physics and Astronomy, University College London, London, UK
82 Louisiana Tech University, Ruston, LA, USA
83 Laboratoire de Physique Nucléaire et de Hautes Energies, UPMC and Université Paris-Diderot and CNRS/IN2P3, Paris,
France
84 Fysiska institutionen, Lunds universitet, Lund, Sweden
85 Departamento de Fisica Teorica C-15, Universidad Autonoma de Madrid, Madrid, Spain
86 Institut für Physik, Universität Mainz, Mainz, Germany
87 School of Physics and Astronomy, University of Manchester, Manchester, UK
88 CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France
89 Department of Physics, University of Massachusetts, Amherst, MA, USA
90 Department of Physics, McGill University, Montreal, QC, Canada
91 School of Physics, University of Melbourne, Victoria, Australia
92 Department of Physics, The University of Michigan, Ann Arbor, MI, USA
93 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA
94 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy
95 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Republic of Belarus
96 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Republic of Belarus
97 Group of Particle Physics, University of Montreal, Montreal, QC, Canada
98 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia
99 Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia
100 National Research Nuclear University MEPhI, Moscow, Russia
101 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia
102 Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany
103 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany
104 Nagasaki Institute of Applied Science, Nagasaki, Japan
105 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan
106 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy
107 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA
108 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The
Netherlands
109 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands
148 (a)Department of Physics, Stockholm University, Stockholm, Sweden; (b)The Oskar Klein Centre, Stockholm, Sweden
149 Physics Department, Royal Institute of Technology, Stockholm, Sweden
150 Departments of Physics and Astronomy and Chemistry, Stony Brook University, Stony Brook, NY, USA
151 Department of Physics and Astronomy, University of Sussex, Brighton, UK
152 School of Physics, University of Sydney, Sydney, Australia
153 Institute of Physics, Academia Sinica, Taipei, Taiwan
154 Department of Physics, Technion: Israel Institute of Technology, Haifa, Israel
155 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel
156 Department of Physics, Aristotle University of Thessaloniki, Thessaloníki, Greece
157 International Center for Elementary Particle Physics and Department of Physics, The University of Tokyo, Tokyo, Japan
158 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan
159 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan
160 Tomsk State University, Tomsk, Russia
161 Department of Physics, University of Toronto, Toronto, ON, Canada
162 (a)INFN-TIFPA, Trento, Italy; (b)University of Trento, Trento, Italy
163 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada
164 Faculty of Pure and Applied Sciences, and Center for Integrated Research in Fundamental Science and Engineering,
University of Tsukuba, Tsukuba, Japan
165 Department of Physics and Astronomy, Tufts University, Medford, MA, USA
166 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA
167 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento di Chimica,
Fisica e Ambiente, Università di Udine, Udine, Italy
168 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden
169 Department of Physics, University of Illinois, Urbana, IL, USA
170 Instituto de Fisica Corpuscular (IFIC) and Departamento de Fisica Atomica, Molecular y Nuclear and Departamento de
Ingeniería Electrónica and Instituto de Microelectrónica de Barcelona (IMB-CNM), University of Valencia and CSIC,
Valencia, Spain
171 Department of Physics, University of British Columbia, Vancouver, BC, Canada
172 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada
173 Department of Physics, University of Warwick, Coventry, UK
174 Waseda University, Tokyo, Japan
175 Department of Particle Physics, The Weizmann Institute of Science, Rehovot, Israel
176 Department of Physics, University of Wisconsin, Madison, WI, USA
177 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität, Würzburg, Germany
178 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal,
Germany
179 Department of Physics, Yale University, New Haven, CT, USA
180 Yerevan Physics Institute, Yerevan, Armenia
181 1211, Geneva 23, Switzerland
182 Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France
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25 Department of Physics, Brandeis University, Waltham, MA, USA
26 ( a)Universidade Federal do Rio De Janeiro COPPE /EE/IF, Rio de Janeiro, Brazil; (b)Electrical Circuits Department , Federal University of Juiz de Fora (UFJF), Juiz de Fora, Brazil; (c)Federal University of Sao Joao del Rei (UFSJ) , Sao Joao del Rei , Brazil; (d)Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil
27 Physics Department, Brookhaven National Laboratory, Upton, NY , USA
28 (a )Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and Nuclear Engineering , Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania; (d)Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies , Cluj Napoca, Romania; (e)University Politehnica Bucharest, Bucharest, Romania; (f)West University in Timisoara, Timisoara, Romania
29 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina
30 Cavendish Laboratory, University of Cambridge, Cambridge, UK
31 Department of Physics, Carleton University, Ottawa, ON, Canada
32 CERN , Geneva, Switzerland
33 Enrico Fermi Institute , University of Chicago, Chicago, IL, USA
34 (a )Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Departamento de Física, Universidad Técnica Federico Santa María, Valparaiso, Chile
35 (a)Institute of High Energy Physics , Chinese Academy of Sciences, Beijing, China; (b)Department of Physics, Nanjing University, Nanjing, Jiangsu, China; (c)Physics Department, Tsinghua University, Beijing 100084, China
36 (a )Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui, China; (b)School of Physics, Shandong University, Jinan, Shandong, China; (c)Department of Physics and Astronomy, Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education, Shanghai Key Laboratory for Particle Physics and Cosmology , Shanghai Jiao Tong University, Shanghai (also at PKU-CHEP), Shanghai, China
37 Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
38 Nevis Laboratory , Columbia University, Irvington, NY , USA
39 Niels Bohr Institute , University of Copenhagen, Copenhagen, Denmark
40 (a)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy; (b)Dipartimento di Fisica, Università della Calabria , Rende, Italy
41 (a)Faculty of Physics and Applied Computer Science , AGH University of Science and Technology, Kraków, Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland
42 Institute of Nuclear Physics, Polish Academy of Sciences, Kraków , Poland
43 Physics Department, Southern Methodist University, Dallas, TX, USA
44 Physics Department, University of Texas at Dallas, Richardson, TX , USA
45 DESY , Hamburg, Zeuthen, Germany
46 Lehrstuhl für Experimentelle Physik IV , Technische Universität Dortmund, Dortmund, Germany
47 Institut für Kern- und Teilchenphysik , Technische Universität Dresden, Dresden, Germany
48 Department of Physics, Duke University, Durham, NC , USA
49 SUPA-School of Physics and Astronomy , University of Edinburgh, Edinburgh, UK
50 INFN Laboratori Nazionali di Frascati , Frascati, Italy
51 Fakultät für Mathematik und Physik, Albert-Ludwigs- Universität , Freiburg, Germany
52 Departement de Physique Nucleaire et Corpusculaire, Université de Genève, Geneva, Switzerland
53 (a)INFN Sezione di Genova, Genoa, Italy; (b)Dipartimento di Fisica, Università di Genova , Genoa, Italy
54 (a )E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy Physics Institute , Tbilisi State University, Tbilisi, Georgia
55 II Physikalisches Institut , Justus-Liebig-Universität Giessen , Giessen, Germany
56 SUPA-School of Physics and Astronomy , University of Glasgow, Glasgow, UK
57 II Physikalisches Institut , Georg- August-Universität, Göttingen, Germany
58 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3 , Grenoble, France
59 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA
60 (a)Kirchhoff-Institut für Physik, Ruprecht- Karls-Universität Heidelberg , Heidelberg, Germany; (b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg , Heidelberg, Germany; (c)ZITI Institut für technische Informatik, Ruprecht- Karls-Universität Heidelberg , Mannheim, Germany
61 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan
110 Department of Physics, Northern Illinois University, DeKalb, IL, USA
111 Budker Institute of Nuclear Physics, SB RAS , Novosibirsk, Russia
112 Department of Physics, New York University, New York, NY, USA
113 Ohio State University, Columbus, OH , USA
114 Faculty of Science, Okayama University, Okayama, Japan
115 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK , USA
116 Department of Physics, Oklahoma State University, Stillwater, OK , USA
117 Palacký University, RCPTM, Olomouc, Czech Republic
118 Center for High Energy Physics, University of Oregon, Eugene, OR , USA
119 LAL , Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
120 Graduate School of Science, Osaka University, Osaka, Japan
121 Department of Physics, University of Oslo, Oslo, Norway
122 Department of Physics, Oxford University, Oxford, UK
123 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia , Pavia, Italy
124 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA
125 National Research Centre “Kurchatov Institute” B.P. Konstantinov Petersburg Nuclear Physics Institute , St. Petersburg, Russia
126 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E . Fermi, Università di Pisa, Pisa, Italy
127 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA
128 ( a)Laboratório de Instrumentação e Física Experimental de Partículas-LIP , Lisbon, Portugal; (b)Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal; (c)Department of Physics, University of Coimbra, Coimbra, Portugal; (d)Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal; (e)Departamento de Fisica, Universidade do Minho, Braga, Portugal; (f)Departamento de Fisica Teorica y del Cosmos and CAFPE , Universidad de Granada, Granada, Spain; (g) Dep Fisica and CEFITEC of Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Caparica, Lisbon, Portugal
129 Institute of Physics, Academy of Sciences of the Czech Republic , Prague, Czech Republic
130 Czech Technical University in Prague, Prague, Czech Republic
131 Faculty of Mathematics and Physics , Charles University, Prague, Czech Republic
132 State Research Center Institute for High Energy Physics (Protvino) , NRC KI , Protvino, Russia
133 Particle Physics Department , Rutherford Appleton Laboratory, Didcot, UK
134 (a)INFN Sezione di Roma , Rome, Italy; (b)Dipartimento di Fisica , Sapienza Università di Roma, Rome, Italy
135 (a)INFN Sezione di Roma Tor Vergata , Rome, Italy; (b)Dipartimento di Fisica , Università di Roma Tor Vergata, Rome, Italy
136 (a)INFN Sezione di Roma Tre , Rome, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy
137 (a)Faculté des Sciences Ain Chock , Réseau Universitaire de Physique des Hautes Energies-Université Hassan II , Casablanca, Morocco; (b)Centre National de l' Energie des Sciences Techniques Nucleaires , Rabat, Morocco; (c) Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Marrakech, Morocco; (d)Faculté des Sciences, Université Mohamed Premier and LPTPM , Oujda, Morocco; (e)Faculté des Sciences, Université Mohammed V , Rabat , Morocco
138 DSM/IRFU (Institut de Recherches sur les Lois Fondamentales de l' Univers), CEA Saclay (Commissariat à l'Energie Atomique et aux Energies Alternatives), Gif-sur- Yvette , France
139 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA
140 Department of Physics, University of Washington, Seattle, WA, USA
141 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK
142 Department of Physics, Shinshu University, Nagano, Japan
143 Department Physik , Universität Siegen, Siegen, Germany
144 Department of Physics, Simon Fraser University, Burnaby, BC , Canada
145 SLAC National Accelerator Laboratory , Stanford, CA, USA
146 (a )Faculty of Mathematics, Physics and Informatics , Comenius University, Bratislava, Slovak Republic; (b)Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice , Slovak Republic
147 (a )Department of Physics, University of Cape Town, Cape Town, South Africa; (b )Department of Physics, University of Johannesburg, Johannesburg, South Africa; (c)School of Physics, University of the Witwatersrand, Johannesburg, South Africa